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Taylor Approximations for Model Uncertainty within the Tweedie Exponential Dispersion Family

Published online by Cambridge University Press:  09 August 2013

Daniel H. Alai  and
Mario V. Wüthrich
Daniel H. Alai
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland, E-mail: daniel.alai@math.ethz.ch
Mario V. Wüthrich
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland, E-mail: mario.wuethrich@math.ethz.ch
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Abstract

The use of generalized linear models (GLM) to estimate claims reserves has become a standard method in insurance. Most frequently, the exponential dispersion family (EDF) is used; see e.g. England, Verrall. We study the so-called Tweedie EDF and test the sensitivity of the claims reserves and their mean square error of predictions (MSEP) over this family. Furthermore, we develop second order Taylor approximations for the claims reserves and the MSEPs for members of the Tweedie family that are difficult to obtain in practice, but are close enough to models for which claims reserves and MSEP estimations are easy to determine. As a result of multiple case studies, we find that claims reserves estimation is relatively insensitive to which distribution is chosen amongst the Tweedie family, in contrast to the MSEP, which varies widely.

Keywords

Claims ReservingExponential Dispersion FamilyModel UncertaintyPower Variance FunctionTweedie's Exponential Dispersion ModelsPrediction Error
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 453 - 477
Copyright
Copyright © International Actuarial Association 2009

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